[amelius]

I have a question about neural networks.

Say, you are training a NN to recognize handwritten characters 0 and 1, and you have 1000 training images for each character (so 2000 images in total). All images are bitmaps with 0 for black and 1 for white.

Now, by accident, all the "0" training-images have an even number of black pixels, and all the "1" training-images have an odd number of black pixels.

How do you know that the NN really learns to recognize 0's and 1's, as opposed to recognizing whether the number of pixels in an image is even or odd?

[mindcrime]

I would say that if you're using a single layer NN, the answer is "you don't really know". And that gets to a point about how we still don't entirely understand how neural networks work, even when they do work.

If you were using a deep network though, and if the current theory is correct, it would be a slightly different story. The current thinking, as I understand it, is that with deep networks, each layer learns representations of certain features (say "slashes", "edges", "right slanted lines", "left slanted lines", etc.) and the progressively higher layers learn representations composed from those more primitive features. So if a deep net were recognizing your handwritten characters, you could probably reason that it isn't just considering whether the number of black pixels is even or odd.

Now in reality this is a pretty contrived, and probably unlikely scenario. But it's a valid question, because there's a deeper point to all of this, which involves transference of learning. That is, how do you take the learning done by a neural network - trained to do one thing - and then leverage that learning in another application. We still don't exactly know how to do that, and that's in part because we don't entirely understand the nature of the representations the networks build up. So a very good answer to your question would arguably help understand how to do transference, which would make NN's even more useful.

[argonaut]

The net is just going to learn the representation "even/odd number of black pixels," if that's the easiest thing to learn.

It also goes without saying that 2k images is probably not going to be enough data to learn any meaningfully general feature representation.

[JoeAltmaier]

They famously do things like that all the time - instead of recognizing a tank in the woods, they notice all the tanks-in-woods pictures were taken on a sunny day; they train to recognize a sunny day.

[rm999]

These kinds of things can happen surprisingly easily in the real-world. The most common cause is "target leaks", which happen when the thing you are trying to predict accidentally ends up in your dataset, usually indirectly through some non-obvious process. Neural networks are especially good learners, and will perform suspiciously well in these situations.

There's often no way to know exactly what a neural network is doing, but sanity checks can catch most issues. Realistically, you wouldn't expect a neural network to perform with 100% accuracy, which would be a first clue in your example.

[narrator]

This is more or less a case of overfitting. The algorithm works on the training set but doesn't generalize well. Tweaking the algorithm by decreasing the number of nodes in the hidden layer and doing cross-validation usually can help with this.

[muizelaar]

You don't necessarily know, but the unlikeliness of this occurring in the training images and the structure of the neural net making it difficult for the net to learn to even or oddness of the number of pixels makes one reasonably confident.

[trhway]

http://joi.ito.com/images2/mathjoke.gif

[Homunculiheaded]

There's actually a case in the early history of perceptrons that brings up this exact issue:

"There is a humorous story from the early days of machine learning about a network that was supposed to be trained to recognize tanks hidden in forest regions. The network was trained on a large set of photographs – some with tanks and some without tanks. After learning was complete the system appeared to work well when “shown” additional photographs from the original set. As a final test, a new group of photos were taken to see if the network could recognize tanks in a slightly different setting. The results were extremely disappointing. No one was sure why the network failed on this new group of photos. Eventually, someone noticed that in the original set of photos the network had been trained on, all of the photos with tanks had been taken on a cloudy day, while all of the photos without tanks were taken on a sunny day. The network had not learned to detect the difference between scenes with tanks and without tanks, it had instead learned to distinguish photos taken on cloudy days from photos taken on sunny days!"[0]

The pragmatic answer is that this is why you have two hold-out sets: cross validation/dev set and the test set. Typically you keep 70% of the data for training, 15% of the data for CV and 15% for Test. Ideally you should shuffle the data enough that there isn't any bias in the natural order of the data.

You train the model on the train data, and estimate how well the model actually performs on the CV set which the model did not see in training. You continue to use the CV set while you tweak parameters, try out new models etc. At this point you may have "cheated" a bit because you only kept things that worked well on your CV data. Finally when you say "this is done!" you try out your model on the Test data set.

Of course it's still possible that you would have the even/odd issue, and the answer to this whole set of issues is "healthy skepticism", and checking for these types of errors.

Take for example this Sentence Completion Challenge from Microsoft Research [1]

They claim some astounding results on correctly predicting GRE type questions using a very simple model (LSA for those who care). These results seemed impossible! But it turns out they cheated by training the model only on possible answers (which is akin to studying for the actually GRE by only review the possible answers that will be on the exam).

We tend to obsess over p-values and test validation scores as a substitute for reasoning. But all research papers should be read as an argument a friend is making to you, "I've done this incredible thing... ", and no single number should replace reasoned inquisition into possible errors.

[0] http://watson.latech.edu/WatsonRebootTest/ch14s2p4.html

[1] http://research.microsoft.com/apps/pubs/?id=157031

[rahimiali]

the tank anecdote is also famously apocryphal. here's a good analysis of the origin of that story: http://www.jefftk.com/p/detecting-tanks

[argonaut]

I'm pretty sure that story is an urban legend. Nobody can find the original source.

[conjectures]

Because you can simulate from the network. If you were right, this couldn't happen:

http://www.cs.toronto.edu/~hinton/adi/index.htm